What are FOCs and SOCs?

Question

I keep seeing the terms first-order conditions and second-order conditions used in my undergrad economics class on production functions, monopolies, etc but I have no idea what these terms mean. It seems like a completely ambiguous term. What kind of conditions? Can someone explain what these terms mean? If it is context dependent, provided some of them most elementary meanings you associate with the term.

Answer 1

These are specific terms related to the use of calculus in math.

With a given formula, we can use calculus to derive a number of additional formula and expressions. For example:

From a given cost function, we can take the first order derivative to find the marginal cost

From a given revenue function, we can take the first order derivative to find the marginal revenue

From a given utility function, we can take the first order derivative to find the marginal utility.

Once you have found the derivative of a function, you can in fact take a second derivative (second order condition) which we often undertake to find whether slopes of lines are positive or negative, or whether they are maximums or minimums.

These are just mathematical tools and techniques then to solve economic problems.